Question: The sum of two numbers is $138$, and their difference is $22$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 138}$ ${x-y = 22}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 160 $ $ x = \dfrac{160}{2} $ ${x = 80}$ Now that you know ${x = 80}$ , plug it back into $ {x+y = 138}$ to find $y$ ${(80)}{ + y = 138}$ ${y = 58}$ You can also plug ${x = 80}$ into $ {x-y = 22}$ and get the same answer for $y$ ${(80)}{ - y = 22}$ ${y = 58}$ Therefore, the larger number is $80$, and the smaller number is $58$.